daytime from surface values of pressure, temperature and relative humidity

We present a formalism that relates the vertical column density (VCD) of the oxygen collision complex O2-O2 (denoted as O4 below) to surface (2 m) values of temperature and pressure, based on physical laws. In addition, we propose an empirical modification which also accounts for surface relative humidity (RH). This allows for simple and quick calculation of the O4 VCD without the need for constructing full vertical profiles. The parameterization reproduces the true O4 VCD, as derived from vertically integrated profiles, within −0.7%±1.2% (mean±SD) for WRF simulations around Germany, 0.2%± 5 1.8% for global reanalysis data (ERA5), and −0.3%± 1.4% for GRUAN radiosonde measurements around the world. When applied to measured surface values, uncertainties of 1 K, 1 hPa, and 16% for temperature, pressure, and RH correspond to relative uncertainties of the O4 VCD of 0.3%, 0.2%, and 1%, respectively. The proposed parameterization thus provides a simple and accurate formula for the calculation of the O4 VCD which is expected to be useful in particular for MAX-DOAS applications. 10